Question

If all the vowels of the word 'TREATMENT' are replaced by its succeeding letter according to the English alphabet and all the consonants are replaced with their previous letter according to the English alphabet and then all the letters are arranged in alphabetical order, then how many letters are there between the third letter from the left and fourth letter from the right in the English alphabetic series?

• A. 6
• B. 12
• C. 9
• D. 10
• E. 11

Hint:

To find the number of letters between two letters with alphabetical positions $P_1$ and $P_2$, use the formula: $|P_2 - P_1| - 1$. For F(6) and Q(17): $|17 - 6| - 1 = 11 - 1 = 10$.

Answer 1

The Correct Option is D

Concept:
This problem involves a three-step transformation: substitution based on character type (vowel vs. consonant), alphabetical sorting of the resulting string, and calculating the gap between two specific positions in the English alphabet.

Step 1: Apply the substitution rules to 'TREATMENT'.
• Vowels (A, E, I, O, U) $\to$ Succeeding letter ($+1$)
• Consonants $\to$ Previous letter ($-1$) Original Word: T R E A T M E N T
• T (Consonant) $\to$ S
• R (Consonant) $\to$ Q
• E (Vowel) $\to$ F
• A (Vowel) $\to$ B
• T (Consonant) $\to$ S
• M (Consonant) $\to$ L
• E (Vowel) $\to$ F
• N (Consonant) $\to$ M
• T (Consonant) $\to$ S New string: S Q F B S L F M S


Step 2: Arrange in alphabetical order.
Sorting the letters: B, F, F, L, M, Q, S, S, S.


Step 3: Identify the target letters and calculate the gap.
• Third letter from the left: The sorted sequence is (1:B, 2:F, 3:F). The letter is F.
• Fourth letter from the right: Counting from the end (9:S, 8:S, 7:S, 6:Q). The letter is Q. Letters between F and Q in the alphabet: G, H, I, J, K, L, M, N, O, P.
Count = 10.